b
\(\lambda \,\, = \,\,\,557\,\,nm\,;\,\,\,\,\,hv\,\, -   h{v_0} = \,\,\,e{V_S}\)

\( \Rightarrow \,hv = h{v_0} - e{V_S} = \left\{ {\frac{{1240}}{{557}} - 0.25} \right\}eV\)

\( = \frac{{1240}}{{{\lambda _{Th}}(nm)}}\)

\( \Rightarrow \,1.976 = \frac{{1240}}{{{\lambda _{Th}}(nm)}}\, \Rightarrow \,\frac{{1240}}{{1.976}} = 627.53\,nm\)